Hybrid summary statistics: neural weak lensing inference beyond the power spectrum
This work addresses the challenge of improving inference accuracy in cosmology, specifically for weak gravitational lensing analysis, by efficiently augmenting traditional methods with neural networks, though it is incremental as it builds on existing Information Maximising Neural Networks.
The authors tackled the problem of extracting more information from weak lensing data beyond the power spectrum by developing a hybrid approach that combines physics-based summaries with neural network summaries, resulting in up to 8 times more information gain in parameter constraints.
In inference problems, we often have domain knowledge which allows us to define summary statistics that capture most of the information content in a dataset. In this paper, we present a hybrid approach, where such physics-based summaries are augmented by a set of compressed neural summary statistics that are optimised to extract the extra information that is not captured by the predefined summaries. The resulting statistics are very powerful inputs to simulation-based or implicit inference of model parameters. We apply this generalisation of Information Maximising Neural Networks (IMNNs) to parameter constraints from tomographic weak gravitational lensing convergence maps to find summary statistics that are explicitly optimised to complement angular power spectrum estimates. We study several dark matter simulation resolutions in low- and high-noise regimes. We show that i) the information-update formalism extracts at least $3\times$ and up to $8\times$ as much information as the angular power spectrum in all noise regimes, ii) the network summaries are highly complementary to existing 2-point summaries, and iii) our formalism allows for networks with smaller, physically-informed architectures to match much larger regression networks with far fewer simulations needed to obtain asymptotically optimal inference.